Peter Koepke

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The Naproche project 1 (NAtural language PROof CHEcking) studies the semi-formal language of mathematics (SFLM) as used in journals and textbooks from the perspectives of linguistics, logic and mathematics. A central goal of Naproche is to develop and implement a controlled natural language (CNL) for mathematical texts which can be transformed automatically(More)
We generalize standard Turing machines working in time ω on a tape of length ω to abstract machines with time α and tape length α, for α some limit ordinal. This model of computation determines an associated computability theory: α-computability theory. We compare the new theory to α-recursion theory, which was developed by G. Sacks and his school. For α an(More)
Using the core model K we determine better lower bounds for the consistency strength of some combinatorial principles: I. Assume that A is a Jonsson cardinal which is 'accessible' in the sense that at least one of (l)-(4) holds: (1) A is a successor cardinal; (2) A = oE and 6 <A ; (3) A is singular of uncountable cofinality; (4) A is a regular but not(More)
Infinite time register machines (ITRMs) are register machines which act on natural numbers and which may run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands, at limits the register contents are defined as lim inf's of the previous register contents. We prove that a real number is computable by an ITRM(More)